ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

doi:10.1007/s10473-019-0209-3

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 429-448.doi: 10.1007/s10473-019-0209-3

ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

王长有¹, 李楠², 周钰谦¹, 蒲兴成³, 李锐³

1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China;
2. Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China;
3. College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

收稿日期:2018-02-22 修回日期:2018-06-28 出版日期:2019-04-25 发布日期:2019-05-06
通讯作者: Nan LI E-mail:2972028881@qq.com
作者简介:Changyou WANG,wangchangyou417@163.com;Yuqian ZHOU,cs97zyq@cuit.edu.cn;Xingcheng PU,puxc@cqupt.edu.cn;Rui LI,liruimath@qq.com
基金资助:
This work is supported by the Sichuan Science and Technology Program of China (2018JY0480), the Natural Science Foundation Project of CQ CSTC of China (cstc2015jcyjBX0135), the National Nature Science Fundation of China (61503053).

ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

Changyou WANG¹, Nan LI², Yuqian ZHOU¹, Xingcheng PU³, Rui LI³

1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China;
2. Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China;
3. College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received:2018-02-22 Revised:2018-06-28 Online:2019-04-25 Published:2019-05-06
Contact: Nan LI E-mail:2972028881@qq.com
Supported by:
This work is supported by the Sichuan Science and Technology Program of China (2018JY0480), the Natural Science Foundation Project of CQ CSTC of China (cstc2015jcyjBX0135), the National Nature Science Fundation of China (61503053).

摘要/Abstract

摘要： This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system. Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.

关键词: predator-prey model, delay, diffusion, permanence, attractivity, periodic solution

Abstract: This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system. Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system.

Key words: predator-prey model, delay, diffusion, permanence, attractivity, periodic solution

王长有, 李楠, 周钰谦, 蒲兴成, 李锐. ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION[J]. 数学物理学报(英文版), 2019, 39(2): 429-448.

Changyou WANG, Nan LI, Yuqian ZHOU, Xingcheng PU, Rui LI. ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION[J]. Acta mathematica scientia,Series B, 2019, 39(2): 429-448.

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ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

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